There have already been many attempts to isomerize .alpha.,.beta.-unsaturated oxo compounds with the aid of bases or acids in order to produce the corresponding .beta.,.gamma.-unsaturated oxo compounds. For example, in U.S. Pat. No. 2,197,462 4-methyl-nona-4-en-6-one has been isomerized in the presence of sodium ethylate in moderate yields to give 4-methyl-nona-3-en-6-one and in U.S. Pat. No. 3,385,903 isophorone has been isomerized with the aid of p-toluenesulfonic acid to give in part .beta.-isophorone. A more precise examination of this latter reaction has demonstrated that with the use of p-toluenesulfonic acid as the catalyst, there is always obtained at best a mixture of equal parts of isophorone and .beta.-isophorone in which the .beta.-isophorone is unstable and is converted at least partly back into isophorone.